Choose the correct answer for the following limit: Select one: Ο Α. 0 O B. Does not exist. OC. None of the others. OD. 2 OE. 13 x³ + 6y² lim (z,y) (0,0) 5x³ + y²

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: The given geometric sequence: 32, 38,332,.....

Q: Evaluate: cot (9) -do None of the choices ɔ+ − ( 7 ) 400 - ( 7 ) 8400 O tan³ () – tan an ( 1 ) - + +…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

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Q: Use the Comparison Test to determine whether the series converges. Σ k=1 1 8 5k° +6

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Q: The solution was wrong. What is the correct solution?

A: Solve the following

Q: the region enclosed by y = e¹¹, y = 5², and a e = 1. Find the area of the region.

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Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: Use Linear Approximation to estimate Af = f (7.01) - f(7) for f(x) = x². (Use decimal notation. Give…

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Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: See this solution in below

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

A: Here we have to find the directional derivative.

Q: 97. Σ n=1 1 2n(n + 1)

A: The given series,     ∑n=1∞12nn+1

Q: Solution is incorrect. Please correct it.

A: dydx=6y18+9x2y18⇒dydx=6y18(1+9x2)⇒y18dy=6(1+9x2)dx

Q: Use the given information to find the exact value of the trigonometric function.  cos θ = 1/4 , csc…

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Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: We have to find the 10th term. The general term geometric progression is given by- an=a1rn-1

Q: Question 2 What is the slope of the tangent line to the graph of x² + 2xy = y² + x = 39 at x = 5…

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Q: Differentiate and simplify this function:  e√t^2+t+1 - e-√t^2+t+1

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Solution is given below:

Q: What is the integral of f sin² x cos² x dx? cos(z) sin³ (2) cos(z) sin(z) + 4 4 ○ sin(4z)+4z 32 +C…

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Q: Consider the function f(x)=5/x^2 - 9/x^7 Let F(x) be the antiderivative of f(x)with F(1)=0 then…

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Q: B a A b Use the right triangle and the given information to solve the triangle. a=2, c = 4; find b,…

A: Let's solve given triangle.

Q: A solid figure projects the same shape on the x-y, y-z, and x-z view. Which of the following…

A: A solid object have same shape on x-y, y-z and x-z view.

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: Evaluate the limit: limo* [cos(3x)]= O e-3 03 e 01 ◄ Previous

A: To evaluate the limit.

Q: Find the arc length of the following curve on the given interval. x= 12t³, y=18t², 0sts √3 The arc…

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Q: A) Solve the given differential equation by separation of variables. B) Find a solution that…

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Q: Estimate the area under the graph of f(x)=1/x+2 over the interval [2,5] using eight approximating…

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Q: Use the Comparison Test or the Limit Comparison Test to determine whether the following series…

A: We need to choose correct option.

Q: Find y': Oy: Oy = Oy' = O y' y cos(xy)+1 x cos(xy)-1 x cos(xy+1) y cos(xy)-1 y cos(xy)+1 x cos(xy)-1…

A: To find the value of y' for the given function.

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: Integrate √1 - r²dr Select one: OA. }(arcsinx+v1_2)+C OB. }(arcsinx+2v1_z)+C OC. (arcsinx +…

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Q: Evaluate the integrals using trigonometric substitution dz 2² √2²-4

A: Find the inegrals by Trignormeric substitution

Q: If the given sequence is a geometric sequence, find the common ratio. 4/3, 8/3, 16/3, 32/3, 64,3

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Q: 14. Show that the demand function D(p) =alp', where a and b are positive real numbers, has a…

A: Solution is given below:

Q: What is f (3) When x²-9 X-3 f(x) = x when XX3? Assume that f(x) is a function that is continuous for…

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Q: What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C None of the choices cos" (2x)…

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Q: Question 12 Find the 2nd derivative (y") of y=√x ln x In 2

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Q: The figure has a tangent line drawn at a labeled point. 9500 9400 9300 9200 9100 p(t) thousand…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.…

A: We have to find area of given region.

Q: Use an appropriate test to determine whether the series converges. k² +3 2 k + 3k +2 2k²+1 Σ k=1

A: The given series,        ∑k=1∞k2+3k+22k2+1

Q: Evaluate the indefinite integral 9ds s ln(88)

A: We can solve this as follows:

Q: 1. The two graphs below (X & Y) show two functions from our library of common functions. For each…

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Q: Consider the function f(x)f(x) whose second derivative is f''(x)=9x+9sin(x)f′′(x)=9x+9sin(x). If…

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Q: Compute the given integral. Enter your answer using exact values. fe-52 dx = +C

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Q: Write the first five terms of the geometric sequence. a 1 = 6; r = 3

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Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

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Q: A screen saver displays 3 cm x 5 cm and then expands it in such a way that the length of the longer…

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Q: Which of the following is a valid triple integral? ⒸSS ſo ſh(e) (5) f(x, y, z) dzdydr h(y,z) flus) f…

A: We have to discuss about valid triple integral.

Q: 2x Given: z = xlny - = + y sinh√x O O O - - 2x+11n4 y³ - 2x+1 In²2 y3 2x+1 in ²2 y³ 1 2x+2 In2 y3…

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Q: if: z = cos 0+isin prove that: 1) 2+1 z+1 2)221 +1 = itan 0 z² = Z

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